Overview of recent work on self-healing in cementitious materials

ABSTRACT

Cracks, especially microcracks, in concrete are of paramount importance to the durability and the service life of cementitious
composite. However, the self-healing technology, including autogenous healing and autonomous healing, is expected to be one
of effective tools to overcome this boring problem. In this paper, we focus on the autogenous healing of concrete material
and a few of recent works of autonomous healing are also mentioned. The durability and the mechanical properties improved
by the self-healing phenomenon are reviewed from experimental investigation and practical experience. Several aspects of researches,
such as autogenous healing capability of an innovative concrete incorporated geo-materials, self-healing of engineered cementitious
composite and fire-damaged concrete, effect of mineral and admixtures on mechanism and efficiency of self-healing concrete
are summarized to evaluate the presented progresses in the past several years and to outline the perspective for the further
developments. Moreover, a special emphasis is given on the analytical models and computer simulation method of the researches
of self-healing in cementitious materials.

Cracks, especially microcracks, are very common and could appear during any stage of the service life of concrete structure.
Cracks can be caused by different factors including structural/excessive loading, plastic/drying shrinkage, harsh environmental
exposure, poor construction procedures and thermal effects. Due to provide an easy path for the transportation of liquids
and gasses which potentially contain harmful substances, cracks may lead to deterioration of concrete and corrosion of reinforcement.
Hence, mechanical performance and durability of concrete structures are reduced. In addition, cracking is aesthetically poor.
Consequently, large costs are involved in inspection, monitoring, maintenance and repair the cracks of concrete structures
every year. Therefore the best way to heal cracks is by triggering a healing mechanism without human intervention upon appearance
of the crack, inspection and monitoring are consequently needed no longer or at a reduced frequency.

Compared to other engineering materials, concrete is unique because it intrinsically contains micro-reservoirs of unhydrated
cement particles which are widely dispersed and available for self-healing. The phenomenon of self-healing in cementitious
materials can be traced back to one century ago (1). In old concrete structures, some cracks being lined with white crystalline material were observed. One such example is
on an 18th century bridge in Amsterdam, where microcracks were self-healed by the recrystallization of calcite (2). Such phenomenon suggested the ability of concrete to self-seal the cracks with chemical products by itself, perhaps with
the aid of rainwater and carbon dioxide in air. In most concrete, particularly those with a low water/cement ratio, the amount
of unhydrated cement is expected to reach 25% or higher (3). These unhydrated cement particles are known to present for a long time in matrix. Thus, under favorable conditions, the
phenomenon of self-healing in concrete is well established (3, 4).

From experimental investigation and practical experience of self-healing phenomena of cracked concrete, two strategies have
proven promising. One is autogenous healing technique, the other is autonomous healing technique. The autogenous healing means
that cracks/damages can be naturally sealed by the self of concrete, like a bone to heal (5). Such healing of micro-cracks is attributed to rehydration of unhydrated cement particles in concrete matrix (6, 7, 8, 9). For autonomous healing in a composite material self-healing capabilities are achieved by the release of encapsulated repair-agent
as a result of cracking from the onset of damage. When cracks happen, the capsules containing self-healing compounds within
the concrete material break and the healing agent is released to heal the cracks (10, 11, 12, 13, 14, 15). Generally, autogenous healing has more advantages than autonomous healing, like economics which is extremely important
for the highly cost-sensitive construction industry (4, 16). In addition, autonomous healing may potentially weaken the strength of materials due to the addition of self-healing capsules.

Due to the attractive potential and practical value, self-healing materials have been intensely investigated over the last
10 years and a significant increase in the number of scientific publications was accompanied (17, 18, 19). Evidence of self-healing to material design was apparent at the first international conference on self-healing materials
which was held in the Netherlands during April 2007. This conference has also been succeeded by the first two books devoted
solely to self-healing materials (20, 21). In 2005 a RILEM technical committee was established charged with investigating self-healing phenomena in cement-based materials,
as stated by Joseph (22). The growing development in the arena of self-healing materials was largely exhibited by the second, third and fourth international
conference on self-healing materials, held in Chicago in July 2009 and in Bath in June 2011, and in Belgium in June 2013,
respectively.

In past several years, the self-healing of cementitious material has been concerned by so many researchers, and a lot of interesting
outcomes and test techniques have been presented. Thus, it is necessary to discriminate and classify the recent works of self-healing.
In this work, we focus on the autogenous healing of concrete material and while a few of recent works of autonomous healing
are also mentioned. The state-of-the-art on the durability and the mechanical properties influenced by the self-healing phenomenon
are first reviewed from experimental investigation and practical experience to categorize the approaches described in the
literature to-date. Autogenous healing capability of an innovative concrete added geo-materials, self-healing of engineered
cementitious composites (ECC) and fire-damaged concrete, effect of mineral and admixtures on self-healing mechanism are summarized
to evaluate the present advances and to outline a perspective for future developments. Recent advances of the analytical models
and computer simulation technology of self-healing research in cementitious materials is also presented.

Autogenous healing of cracks in fractured concrete has been firstly noticed by the French Academy of Science in 1836 in water
retaining structures, culverts and pipes (23). According to Hearn (8) the self-healing phenomenon was firstly studied by Hyde (24) at the end of the nineteenth century. Previous researchers have investigated the necessary conditions for autogenous healing
in concrete materials. These studies had resulted in identifying three general criteria critical to robust self-healing: the
presence of specific chemical species (7, 25, 26), exposure to various environmental conditions (9, 26, 27, 28), and small crack width (9, 25, 29, 30). Meanwhile, it was reported that there were several processes including chemical, physical and mechanical interactions as
discussed by Kishi et al. (31) to be responsible for autogenous healing. Among these reasons of autogenous healing in cementitious composites, it was clarified
that crystallization of calcium carbonate within the crack fracture surface was the main mechanism for self-healing of matured
concrete (9). Specifically, a calcite formation in the area of water-bearing cracks takes place in the material system CaCO3-CO2-H2O according to the following reactions [1, 2] (9, 27)

The water-insoluble CaCO3 is evolved from a reaction between the calcium ions Ca2+, derived from the concrete, and the in-water available bicarbonates HCO3−, or carbonates CO32−. Furthermore, water temperature, pH value of the water and CO2 partial pressure in the water favor the CaCO3 precipitation in the crack.

Over recent years researchers have investigated the influence of autogenous healing on the durability of cementitious composites.
Many experimental results and practical experiences have demonstrated that cracks in concrete have the ability to heal themselves
and water flow through cracks was reduced with time. Self-healing of leaking cracks was extensively studied by Clear (32), Hearn (8, 23, 33) and Edvardsen (9). As shown in Figure 1, Otsuki (34) suggested that self-healing of microcracks could have been the reason for densification of the concrete cover, thus reducing
the rate of migration of chloride ions into the concrete. In the study of water flow through cracked concrete under a hydraulic
gradient, Edvardsen (9, 25) noted a gradual reduction of permeability over time, again suggesting the ability of the cracked concrete to self-seal itself
and slow the rate of water flow. The main cause of self-healing was attributed to the formation of calcium carbonate, a result
of reaction between unhydrated cement and carbon dioxide dissolved in water (9). Furthermore, Edvardsen (9) concluded that the formation of calcium carbonate responds to two different crystal growth processes under water exposure,
i.e., the kinetics of surface controlled crystal growth in the initial phase and later a diffusion controlled crystal growth.
The observations under ESEM and XEDS confirmed (35) that the microcracks in the specimens submerged in water were healed with significant amount of calcium carbonate, very
like due to the continuous hydration of cementitious materials. Analyses of experimental results showed that there existed
a damage threshold for self-healing both for high strength concrete and normal strength concrete (36). When the damage degree is less than the threshold, the self-healing ratio of concrete is increased with the increase in
damage degree; while the threshold is exceeded, the self-healing ratio is decreased with the increasing of damage degree.
Reinhardt (25) established the dependency of permeability and self-healing behavior of cracked concrete on temperature. For a cause of
reduced chloride ingress, self-healing of microcracks has also been suggested by Fidjestol (37), Bakker (38), Sahmaran (39) and Li (40). Recently, Ismail (41) also confirmed that in the case of crack width below 60 μm, the self-healing potential of the mortar matrix can impede the
effective chloride diffusion along a crack path.

Concrete exposed to high temperatures undergoes a reduction in performance, such as a decreased load-carrying capacity and
durability due to thermo-mechanical and thermo-hydral processes, which result in cracking, loss of strength, and explosive
spalling (42). Re-curing fire-damaged concrete in water can partly restore strength and durability performance (43, 44, 45). Moreover, high-strength concrete was found to have better recovery under re-curing due to its microstructure (46). Hence, the self-healing fire-damaged cementitious composite is becoming an attractive issue for researchers. Henry (42) investigated the loss and recovery of strength and the crack self-healing for normal-and high-strength mortars subjected
to fire damage, and he proposed that recovery mechanism was contributed to the chemical rehydration and full self-healing
of cracks. Durability (air permeability and carbonation resistance) of fire-damaged concrete was recovered under water re-curing
conditions, even if re-curing in air resulted in a lower durability performance than re-curing in water. The decreases of
air permeability and the increases of carbonation resistance under water and air-water conditions were attributed to crack
healing and porosity recovery of specimens. However, although porosity recovers to pre-fire levels after water and air-water
re-curing and crack self-healing was observed, the pre-fire compressive strength, complete strength recovery, was not reached.
In the meantime, the microcracks that were formed due to quenching were mostly healed within 7 days of water recurring and
porosity was found to recover to pre-fire levels. Chemical analyses found that under water re-curing conditions, the crystalline
structure and amounts of chemically bound water and Ca(OH)2, one of the primary hydration products, returned to pre-fire levels. The instability of the healed cracks and rehydrated
pore structure resulted in strength reduction even though the crystalline structure, amount of hydration product, and porosity
were found to recover to pre-fire levels and crack self-healing was also observed. Henry concluded that weaknesses or flaws
exist in the newly healed crack interface that could not be detected by visual observation but still produced an improvement
in durability. Furthermore, water re-curing could not fully recover compressive strength due to this instability, the air
permeability and carbonation rate were significantly reduced due to crack self-healing and a reduction in porosity which reduce
mass transport ability. However, damage in the interface between the mortar and coarse aggregates and recovery properties
in fire damaged concrete need to be solved.

Several experimental results have confirmed that the recovery of mechanical properties can be attained to some extents due
to the self-healing in cementitious materials. For example, the recovery of flexural strength was observed in pre-cracked
early age concrete beams while clamped and submerged in water (47). More recent work by Heide (48), as overviewed by Ghosh (20), has therefore focused on examining both the mechanical strength gain and reduction in permeability of early-age concrete
which has been cracked and allowed to heal autogenously. Furthermore, it was observed that recovery of many mechanical related
properties was possible after water immersion, e.g. the stiffness of pre-cracked specimens (49) and the compressive strength of pre-damaged cylindrical specimens (50). The self-healing observed from these investigations was associated with continued hydration of the unhydrated cement in
cementitious materials. On the other hand, Granger (51) carried out an experimental program of mechanical test on ultra-high performance concrete and concluded that the self-healing
of the pre-existing crack was mainly due to hydration of anhydrous clinker on the crack surface and that the stiffness of
newly formed crystals is close to that of primary C-S-H. Joseph (22) concluded that the compressive stress applied to the crack faces was found to be very beneficial in respect to closing the
initial crack, which was typically 50 μm wide. However, additional compressive forces above that required to cause crack closure
and reinstate contact between the crack faces did little to improve the strength recovery following healing. As indicated
above, the phenomenon of autogenous healing has been demonstrated to be effective for the recovery of mechanical properties.

The use of compressive forces to close cracks and to create contact between crack faces has been shown to be an effective
approach to enhancing the natural autogenous healing process within cementitious materials (20, 48). Recently work undertaken at Cardiff University in UK has therefore examined the feasibility of low-level post-tensioning
of cementitious materials using shrinkable polymer tendons to enhance autogenous healing behavior (22, 52). The system involves the incorporation of unbonded pre-oriented polymer tendons in cementitious beams. Post-tensioning is
achieved by thermally activating the shrinkage mechanism of the restrained polymer tendons after the cement-based material
has undergone initial curing. The concept has been investigated by using tendons formed from shrinkable polyethylene terephthalate
(PET). The basic concept of material system is illustrated in Figure 2. Jefferson (52) has shown that the shrinkage activation of the PET tendon was sufficient to completely close the 0.3 mm crack created during
the initial three-point loading on day 4. Furthermore, the reloading test data on day 8 indicated that not only had the restrained
shrinkage of the tendon caused the crack within the mortar beam to completely close but it had also put the beam into compression.
This new composite shape memory polymer cementitious system also had the potential to offer crack prevention in addition to
crack healing, if the integral polymer tendons were activated prior to the occurrence of early-age cracking. However, crack
closure through the external application of compressive forces in situ is impractical, and some improvement for this apparatus
is necessary if active roles are expected to close the cracks in cementitious matrix.

Based on the principle of autonomous healing in materials, an autonomous healing system that once breaking, the glass capillary
tubes release cyanoacrylate into the crack plane which flows rapidly, under the influence of attractive capillary forces,
across the two crack faces was developed in concrete material by Joseph (53, 54), as demonstrated in Figure 3. The autonomous healing system offered a successful mechanism for restoring and in certain circumstances enhancing the mechanical
properties of the composite. The infiltration of the cyanoacrylate reduced the permeability and therefore improved the durability
of the new composite material. The rapid flow and curing ability of the low viscosity cyanoacrylate, which is evident in the
primary healing strength gain, also suggests that this healing system might be applicable to healing damage created under
dynamic situations, such as in earthquakes. Other recent work of autonomous healing in concrete can be referred in (12, 55, 56, 57).

Figure 3. Schematic illustration of the main forces acting on an internally encapsulated healing agent (54).

In the literature of self-healing, many different types of admixtures had been investigated to consider the healing efficiency
of cracks in concrete. In these works, some of them focused on mechanical behavior, some focused on durability and others
focus on microstructure. An interesting recent development has been the autogenous healing of expansive concretes by Hosoda
et al. (58), Kishi et al. (31) and Yamada et al. (59). They have found that the inclusion of expansive agents in the concrete has allowed even large cracks of up 0.3–0.4 mm to
heal (58). Furthermore, the addition of small amounts of various carbonates such as bicarbonate of soda also increased the self-healing
ability of the concrete due to more calcium carbonate to be precipitated (59).

After the investigation of self-healing capability of cementitious composites with different admixtures such as chemical admixture,
expansive agents and geo-materials, a self-healing concrete with normal water/binder ratio was developed and applied as a
new method for crack control and enhanced the service life in concrete structure (60). Furthermore, this self-healing concrete was fabricated in factory and used for the construction of artificial water-retaining
structures and actual tunnel structures. Crack-width of 0.15 mm was self-healed after re-curing for 3 days and the crack width
decreased from 0.22 mm to 0.16 mm after re-curing for 7 days. Water permeability coefficient of self-healing concrete was
significantly lower than that of conventional concrete. Meanwhile, the cracking sensitivity of developed self-healing concrete
was similar to expansive concrete and has a better cracking resistance than normal concrete. Ahn (60) concluded that self-healing of the developed concrete occurred mainly due to the swelling effect, expansion effect and re-crystallization
and the utilization of appropriate dosages of geo-materials allowed a high potential for the repairing of cracked concrete
under the water leakage of underground civil infrastructure such as tunnels.

Additional water is essential for the mechanism of autogenous healing, but in some cases this is a problem when the availability
of water is limited. Meanwhile, fly ash is a pozzolanic material that reacts with Ca(OH)2 from cement hydration and produces C-S-H gel. Significantly, this reaction is less influenced by the availability of free
water than the hydration reaction of cement. Termkhajornkit (61) investigated the self-healing ability of fly ash–cement paste due to the autogenous shrinkage cracking in a sealed curing
condition after 28 days. Experimental results showed that the fly ash–cement system had the self-healing ability for shrinkage
cracks. The self-healing ability of fly ash–cement paste increased as the replacement ratio of fly ash increased from 0% to
50% by volume. Hence, hydrated products from fly ash might seal the cracks and prolong the service life of materials. However,
the self-healing ability, the efficiency and the mechanical property recovery of ordinary concrete added fly ash require to
be further explored.

Self-healing capability of fiber reinforced cementitious composites was also attractive and investigated by many researchers,
such as Li (10) and Homma (62, 63, 64). Especially, ECC has been fast developed in recent years as an extremely durable and environmentally friendly material.
Given the well-controlled crack width, Li and coworkers (4, 65) have investigated the self-healing behavior of ECC under a number of exposure conditions. In their experiments, deliberately
pre-cracked ECC specimens were exposed to various commonly encountered environments, including water permeation and submersion,
wetting and drying cycles, and chloride ponding. The mechanical and transport properties can be largely recovered, especially
for ECC specimens preloaded to below 1% tensile strain. Besides the small crack width, the low water/binder ratio in addition
to the large amount of fly ash in their mixture also helps promote self-healing via continued hydration and pozzolanic activities.
Based on experimental results, Şahmaran (39) proposed that micro-cracks of ECC can be easily closed by autogenous healing process even after exposure for 30 days to
NaCl solution. The observed autogenous healing in ECC added fly ash can be attributed primarily to the large fly ash content
and the relatively low water to binder ratio within the ECC mixture (39, 50, 66, 67, 68). Both transport properties, permeability, and chloride diffusion, showed a decrease over time not only due to the tight
crack width but also the presence of self-healing of the micro-cracks. From these studies, it was apparent that self-healing
both in the mechanical and transport sense was present in ECC. Recent work (64) showed that many fine fibers of polyethylene (PE) were bridging over the crack and crystallization products became easy
to be attached due to the PE fibers, even though crack width reached 100 μm. However, in the place of steel cord bridging
of cementitious composite, the deposition of crystallization products was not seen. Similarly, when crack width was too wide,
little attachments of the crystallization products could be confirmed. Therefore amount of the PE fibers per volume has a
great influence on the self-healing if the crack width was well-controlled. Also, polyvinyl alcohol (PVA) fibers in ECC provide
nucleation sites for healing products that may aid in the self-healing of ECCs.

Self-healing of ECC has been concerned by many researchers in recent years (16, 35, 69, 70, 71, 72). The resonant frequency measurements and the permeability measurements together suggested that autogenous healing within
cementitious materials can be achieved, provided that damage must be restricted to very tight crack widths, below 150 μm and
preferably below 50 μm, at least under 10 wet–dry cycles exposure regime (69). The microstructures of ECC specimens before and after self-healing are shown in Figure 4 (a) and (b). Further, the majority of autogenous healing products are characteristic of calcium carbonate crystals from image analysis
results. Specifically, C-S-H is the main self-healing product for crack widths of 15 μm, and C-S-H and CaCO3 are the main self-healing products for crack widths of 30 μm. Less self-healing product is seen at crack widths of 50 μm;
however, below this width, cracks can be almost completely healed (71). It is believed that rehydration and the formation of CaCO3 crystals are the main reasons for the self-healing phenomena and exposure of crack damaged specimens to wet-dry cycles was
the most effective promoter of self-healing.

Figure 4. Microcracks in ECC before and after self-healing, (a) Before self-healing, (b) After self-healing (69).

Autogenous healing of early ages (3 days) ECC damaged by tensile preloading was investigated by Yang (16). Comparison of the self-healing characteristics of the early age (3 days) specimens with those of more mature specimens
at 90-day age or older, it found that higher stiffness recovery magnitude was attained in mature specimens than in young specimens.
Figure 5 shows the percentage stiffness recovery for the 3-day age specimens as well as those for 6-month old specimens, after pre-damage
to different levels, and then allowed to undergo re-healing with identical cycles of wetting and drying. The recovery decreased
with increasing damage level for the young specimens, dropping from 100% at 0.3% pre-damage to about 10% recovery at 3% pre-damage.
For the more mature specimens the recovery was remarkably maintained at approximately 80% for all four levels of pre-damage
(0.5%, 1.0%, 2%, 3%). The author has pointed out that, for the same imposed (pre-damage) strain, the younger specimens tended
to develop a smaller number of cracks of a larger averaged width compared to mature specimens, while the mature ECC accommodated
a larger number of cracks and maintained a tight crack width on average. Regardless of age, a common trend was also observed
that smaller cracks (less than 20 μm width before healing took place) tended to be more completely filled with C-S-H gels,
while the larger cracks (50 μm or larger) tended to be partially filled with a mixture of C-S-H gels and calcite particles
after the same exposure condition resulting in incomplete healing.

Figure 5. Stiffness recovery on autogenous healing for 3-day and 6-month age ECC specimens, subjected to various pre-damage levels (16).

An interesting approach on self-healing capability of ECC was proposed by Qian (70). Inspired the concept of nanoclay proposed, nanoclay was added in the mixtures to investigate its feasibility to act as
internal water reservoirs to promote self-healing behavior of ECC, eliminating the dependence on the external water supply.
Due to the water retaining capacity of nanoclay to internally cure and heal the damage along the microcracks, the air cured
sample showed reasonable recovery of deflection capacity and the flexural strength increased at the age of 14 days and 28
days. So it was promising to utilize nanoclay as distributed internal water reservoirs to promote self-healing behavior within
ECC without relying on external water supply. According to the procedure and thoughts of their work, it seems that nanoclay
can be considered as a catalyst in the embedded capsule self-healing strategy and unhydrated cement particle as self-healing
agent (73, 74, 75, 76). In some sense of methodology, there exists a consistence between autogenous healing and autonomous healing.

Experimental research has revealed the feasibility and the recovery of mechanical properties for self-healing concrete. However,
it is generally not difficult to directly extract the quantitative measurements such as the autogenous healing efficiency
of unhydrated cement nuclei and the exact dosage of healing agent for autonomous healing approach in terms of experimental
methods. Simulation and modeling tools as well as various analytical approaches provide a powerful extension of traditional
experimental investigations and offer an alternative to at least partly overcome these deficiencies.

Using an advanced history dependent contact model for DEM simulations, Herbst (77) proposed a model for local self-healing that allows damage to heal during loading such that the material strength of the
sample increases and failure/softening is delayed to larger strains. By a concurrent algorithm-based computer simulation system
with the acronym SPACE (Software Package for the Assessment of Compositional Evolution), He (78, 79) investigated the influences of water/cement ratio and cement fineness on the structure of unhydrated cement nuclei that
is underlying concrete’s self-healing capacity in hardened cement paste. Compared to fineness of cement, water/cement ratio
is the dominating factor for the self-healing capacity of concrete. Based on the concept of autonomous healing and elementary
principles from probability theory, Zemskov and Jonkers (80, 81) have recently developed analytical models for computation of the probability that a crack hits an encapsulated particle.
The analytical models (random placement mode of capsules in a layered structure and fully random placement mode of capsules
in bulk material) allowed to estimating combinations of crack lengths, capsule size, and mean intercapsule distance in order
to analyze the efficiency of a self-healing material. However, their models are restricted in two-dimensional case. For three-dimensional
case, further work need to do.

For investigation of the self-healing phenomenon on healing the cracks of matrix, it is necessary to consider the self-healing
efficiency or amount of the rehydration product of unhydrated cement nuclei. Based on two practical different cracking modes
of unhydrated cement nuclei, i.e., splitting crack mode and dome-like crack mode as respectively illustrated in Figure 6 and Figure 7, theoretical models on the self-healing efficiency of rehydration reaction of the unhydrated cement nuclei were developed
by Lv (82, 83, 84). Recurring to a generalized hydration reaction model of cement particles and the particle size distribution of cement approximated
by Rosin-Rammler function (85, 86), the self-healing efficiency model quantitatively considered the influence of the volume fraction, particle size distribution
and cracking modes of unhydrated cement nuclei randomly distributed in hardened cement paste. Generally speaking, for unhydrated
cement particles on a specific crack surface, splitting crack mode and dome-like crack mode may occur together. Hence, for
considering the efficiency due to rehydration of unhydrated cement nuclei, the total self-healing efficiency should was commonly
developed based on the two different cracking modes. Furthermore, the reliability of these theoretical models was verified
via computer simulation technology and the simplified self-healing process was also simulated. It showed that based on the
different cracking mode of unhydrated cement nuclei randomly distributed in the matrix, the self-healing efficiency had a
distinction even for the same particles size distribution. However, the specific rehydration reaction of unhydrated cement
particles left in matrix should be well considered to determine the healing efficiency of autogenous healing.

For determining the exact dosage of capsules incorporated via autonomous healing, several intersecting models of cracks and
capsules had been presented for regularly distributed crack patterns in cementitious composite. Before loading or at the initial
stage of service, both the number and the size of cracks generally are small. In other words, the crack spacing could be larger
than the size of capsule. Of course, the crack may propagate with the increase of loading or the service time. However, it
is expected to heal the defects in matrix before micro-cracks become macro-cracks. Consequently, based on the assumption that
the crack spacing is larger than the length of capsule embedded, short capsules model were developed by Lv (89, 90) to determine the exact dosage. Meanwhile, the long capsules model for dosage of capsules required was also presented to
investigate the autonomous healing in cementitious composite (91, 92). Based on a general assumption that the capsules are randomly dispersed in the matrix and the cracks of matrix appear to
be certain layout or special orientation, Lv (89, 90) developed the analytical model on determining the dosage of capsules embedded to heal the cracks of cementitious composites.
Specifically, the outer/inner cracks in materials caused by different type of mechanisms were simplified to linear cracks
in a two dimensional surface model, or planar cracks in Figure 8(a) and zonal cracks in Figure 8(b) in a three dimensional model. Then, by combining the geometrical probability theory with binomial probability distribution,
the theoretical solutions on the exact dosage of capsules required to completely repair the cracks for specific crack patterns
were developed. For example, considering the crack pattern as shown in Figure 8(b), assume that there are parallel planar cracks with a width of wcrack and the crack space is d, and capsules K containing repair-agent are randomly dispersed in cementitious matrix. Moreover, let lcap, rcap be the length and the radius of the cylindrical capsule K and a capsule K can repair the crack with a fixed volume Vheal in matrix. Concerning to this crack pattern, how to determine the number of capsules completely repairing those zonal cracks
in sampling region was investigated by authors from the viewpoint of geometrical probability (90). After a series of computation and transformation, it was expected that the lowest volume fraction VV of capsules required in per unit volume of cementitious matrix is expressed as [3]

At the same time, the reliability of those proposed theoretical solutions was verified via computer modeling technology. The
authors also presented the hitting probability model of a crack intersecting with capsules when cracks randomly occurred and
capsules with healing agent were disorderly dispersed in the matrix (93). These theoretical models and analytical solutions were expected to quantitatively characterize the self-healing efficiency
of unhydrated cement nuclei or dosage of healing agent required and to be facilitating the experimental research.

A review of current work in the arena of self-healing cementitious materials including autogenous healing and autonomous healing
was presented. Attentions were paid to autogenous healing capability of an innovative concrete added geo-materials, self-healing
of engineered cementitious composites and fire-damaged concrete, modeling and simulation of self-healing phenomenon, effect
of mineral and admixtures on mechanism and efficiency of self-healing concrete. Self-healing cementitious material is promising
to improve their long-term performance, service life and durability problems due to cracking. The development of self-healing
concrete potentially offers great benefit to the construction industry and potentially massive savings to the annual amount
of cost on repair and maintenance of concrete structures in the future.

Compared to autogenous healing, much more issues for autonomous healing want to be solved. First, it is difficult to determine
the critical dosage of capsules in practical experiments and applications based on various actual conditions in cementitious
composite. Second, how to select the self-healing agent, optimize a critical size and geometrical shape of capsules and guarantee
the compatibility of agent used in cementitious materials. The long term durability of concrete materials healed by autonomous
healing is also vacant. However, the methodology of computer simulation and modeling method are recommended for these problems
from recent work of autonomous healing in cementitious composites.

To improve the efficiency of autogenous healing and mechanical properties, some novel techniques were developed such as the
post-tensioning of cementitious materials using shrinkable polymers, incorporating the nanoclay and PVA fibers. Those approaches
have deed facilitated the occurrence of self-healing behavior and have improved the efficiency. Meanwhile, autogenous healing
concrete could be optimized if free water (i.e. nanoclay), a critical crack width, fibers control the cracks and good curing
environment are available in the mixture. Of course, the intrinsic or natural character of cementitious materials has to be
taken into account in designing autogenous healing concrete, such as a relatively high water-binder ratio and the low efficiency
of rehydration of unhydrated cement nuclei. The autogenous healing of cementitious materials not only offers a immediately
promising solution to crack repair and improves the long-term durability and service life, but also consumes the anthropogenic
CO2 emissions, which jeopardize the conditions of earth and are harm for humans’ life.